With centre-backs Harry Maguire (suspended), Raphaël Varane and Lisandro Martinez (injured), Victor Nilsson Lindelöf got the chance from the start in the United defence.
The Swede was highly involved in ensuring that the first half did not offer the Wembley crowd any great entertainment.
Ball-savvy Brighton controlled most of the game and came close to an early lead when Alexis Mac Allister tested David De Gea with a free-kick which the Spaniard cleared.
Otherwise, it was a counter-attacking Manchester United that created the best chances. Bruno Fernandes came close both once and twice, and perhaps Christian Eriksen should have finished better when given space in the penalty area. The shot instead went straight to Robert Sánchez.
The goalkeepers impressed
In the second half, the roles were somewhat reversed as United ate into the match and gradually took over, while Brighton created the best chances.
David De Gea had to make two fine saves after attempts from Julio Enciso and Solly March.
There were no goals and the match went to extra time.
After a rather uneventful first half, Marcus Rashford was incredibly close to breaking the deadlock, but now it was Sánchez’s turn to parry.
Nilsson Lindelöf decided
The second was also goalless and penalties had to decide the event.
After six bombproof penalties each, Solly March shot high over. That gave Victor Nilsson Lindelöf the chance to push United on.
The Swede did not disappoint with a sure penalty and thus awaits the Manchester derby in the final. It will be played on June 3 at Wembley.